# Questions tagged [self-study]

A routine exercise from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for such questions rather than complete answers.

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### Validity of confidence interval for $\rho$ when $X\sim N_3(0,\Sigma)$ with $\Sigma_{ij}=\rho^{|i-j|}$

Suppose $X\sim N_3(0,\Sigma)$, where $\Sigma=\begin{pmatrix}1&\rho&\rho^2\\\rho&1&\rho\\\rho^2&\rho&1\end{pmatrix}$. On the basis of one observation $x=(x_1,x_2,x_3)'$, I ...
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### MLE, regularity conditions, finite and infinite parameter spaces

The problem I have is in figuring out why the MLE is no longer consistent in countable parameter spaces under conditions specified below. The set up is as follows: we are consider a parameters space ...
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### Understanding equation used by Hastie et al

I am trying to recreate FIGURE 3.6 from Elements of Statistical Learning. The only information about the figure is included in the caption. I am not clear on what the equation on the Y-axis means ...
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### Rao-Blackwellization in variational inference

The Black box VI paper introduces Rao-Blackwellization as a method to reduce the variance of the gradient estimator using score function, in section 3.1. However I don't quite get the basic idea ...
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### Sufficient statistics for $\mu_1 - \mu_2$

If $X_1, ..., X_n$ is a random sample from $X \sim N(\mu_1, \sigma^2)$ and $Y_1,..., Y_n$ is a random sample from $Y \sim N(\mu_2, \sigma^2),$ if the samples are independent and $\sigma^2$ is known,...
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### Help understanding a paragraph in Kadane's book Principles of uncertainty

Consider two infinite sequences of indicators of events, $s_1$ and $s_2$, with respective relative frequencies $l_1$ and $l_2$, where $l_1\neq l_2$. Let $A$ be the indicator of an event not an ...
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### Exercise on Borel Cantelli Lemma ($\limsup X_n/ \ln(n) =1$ a.s.) help required to rigorously write the statement

I hope this question is within the scope of this site. Please note that I have solved this Exercise, I do have doubts about my presentation though and about how to rigorously empathize on the ...
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### Dealing with auxiliary random variables for Mean-Field Variational Inference in Bayesian Poisson factorization

I am studying as a part of a class assignment a recent paper on Poisson factorization. Some points of the paper regarding the usage of some auxiliary variables are not clear to me. I would like to ...
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### Question 10.9 from Bayesian Data Analysis, what does accuracy mean here?

I'm doing an independent study in Bayesian Statistics following some chapters from BDA3. When solving the first question from Ch 10 I got stuck. It says: [If] a scalar variable $\theta$ is ...
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### How to show a UMVUE exists only if $g(p)$ is a polynomial of degree at most $n$?

Let $X\sim Bin(n,p)$. The problem is to show that a UMVUE can exist for $g(p)$ only if $g(p)$ is a polynomial in $p$ of degree at most $n$. For the case when $g(p) = \frac{1}{p}$ we can show that it ...
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### Partitioned regression model: estimator of beta 1

below is an exercise that is really giving me a hard time, I believe that there is a simple way around it but I can not find it: Assume the correct regression model is Y = X$\beta$ + $\epsilon$ for E(...
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### French website Providing Instruction/Tutorials on Statistical Theory

This is somewhat of an odd question for CV, but since it's a question about statistical education, I think it falls within the scope of CV. Several years ago I stumbled across a French website that ...
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### Deriving priors for MCMC implementation

I have been working on an assignment lately wherein the object is to implement an MCMC approach to simulate from a generated posterior distribution. The posterior distribution is generated from a ...
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### Conjugate of Weibull with shape known

This isn't exactly a homework problem but rather a self-selected problem I'm doing to prepare for a midterm. I can see from Wikipedia that it is an inverse gamma but I am unable to reach the ...
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### What is the likelihood function of this random variable (beta distribution parameterizing a Bernoulli distribution)?

This is related to an earlier self-study question of mine. The setup is that there are $N$ individuals, indexed by $i$, and two time periods. Individuals choose whether to "invent" something in the ...